Experimenting with Infinite Groups, I

DOI10.1080/10586458.2004.10504558zbMath1083.20024OpenAlexW1973128482MaRDI QIDQ4663080

George Havas, Gilbert Baumslag, Sean Cleary

Publication date: 30 March 2005

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1109106441

zbMATH Keywords

word problemfinitely presented groupsinfinite groupsfinite quotientsisomorphism problemconjugacy problemparafree groupsrelatively free groupsinner automorphism problemnumbers of epimorphisms onto finite groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Automorphisms of infinite groups (20E36) Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Residual properties and generalizations; residually finite groups (20E26) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items (6)

Applications of the Alexander Ideals to the Isomorphism Problem for Families of Groups ⋮ Experimenting with Infinite Groups, I ⋮ Solving the isomorphism problems for two families of parafree groups ⋮ Profinite Rigidity in the SnapPea Census ⋮ Twisted Alexander ideals and the isomorphism problem for a family of parafree groups ⋮ Parafree metabelian Lie algebras which are determined by parafree Lie algebras

Uses Software

• GAP

Cites Work

• The equation \(a^2b^2=c^2\) in free groups
• The equation \(a_ M=b^ Nc^ P\) in a free group
• The Magma algebra system. I: The user language
• Diophantine geometry over groups. II: Completions, closures and formal solutions
• The isomorphism problem for hyperbolic groups. I
• Diophantine geometry over groups. I: Makanin-Razborov diagrams
• Identical relations in groups. I
• On a Problem of Lyndon
• Tarski’s problem about the elementary theory of free groups has a positive solution
• The isomorphism problem for a class of para-free groups
• Experimenting with Infinite Groups, I
• Computational approaches to combinatorial group theory
• Some groups that are just about free
• More groups that are just about free
• On the residual nilpotence of certain one‐relator groups

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